Germany international Badstuber is certain to miss Wednesday's German Cup second-round match against Kaiserslautern as well as Saturday's league game at Hamburg and their Champions League encounter with France's Lille on November 7.
"This is a big setback for us. I hope we can adequately replace him for this period," Bayern coach Jupp Heynckes said.
The Bavarians could also be without Franck Ribery on Wednesday with the winger still feeling the effects of a minor muscle problem.
"He upped the intensity level in training today but he is still doubtful," the club said in a statement.
Bayern are four points clear at the top of the Bundesliga despite Sunday's defeat with Schalke in second place.